Carl had 300 buttons. ³₅ were red and the rest were white and brown. The ratio of the number of white buttons to the number of brown buttons was 1 : 4. Carl decided to give away some red buttons to decrease the number of red buttons to half of the total number of buttons.

1. How many more red buttons than white buttons did he have at first?
2. How many red buttons did he have to give away?

Red buttons	White buttons	Brown buttons	Total
3x5	2x5
	1x2	4x2
15 u	2 u	8 u	300

	Red buttons	White buttons	Brown buttons
Before	15 u	2 u	8 u
Change	- ?
After	10 u	10 u
Comparing red, white and brown buttons in the end	1	1

(a)
The total number of white buttons and brown buttons is repeated. Make the total number of white buttons and brown buttons the same.  LCM of 2 and 5 is 10.

Total number of buttons at first
= 15 u + 2 u + 8 u
= 25 u

25 u = 300

1 u = 300 ÷ 25 = 12

Number of more red buttons than white buttons at first
= 15 u - 2 u
= 13 u
= 13 x 12
= 156

(b)
Number of more red buttons that Carl had to give away
= 15 u - 10 u
= 5 u
= 5 x 12
= 60

Answer(s): (a) 156; (b) 60